Is condensation on a flat roof drain enough to cause a "leak"

Is it possible for there to be enough condensation on a copper or cast iron roof drain pipe to cause enough dripping so that it looks like the roof is leaking? Drywall is stained and water is dripping, but it is sporadic. Doesn't always leak when it is raining.

1. uninsulated ceiling space
2. flat roof copper spun drain.
3. I will assume copper or cast iron drain pipe as it is fairly old commercial building
4. outdoor temps are between 0 and 5 degrees celcius
5. No plumbing pipes in the ceiling space.

Depending on the interior humidity levels, it is entirely possible that if enough moist air came in contact with a cold pipe that it would sweat. It all depends on the humidity levels and the dew point...think iced tea at the beach...the glass will get quite wet. A leak could also be in the picture. Insulating the pipe to prevent the humid air from coming in contact with the pipe should prevent this, but won't help with a leak.

look at sevral things, 1,all tar work on roof esp corners.seams,couping.2,flat roofs only last 10 15 years tar breaks down in 5yrs 3, flat roofs with wood carrier beams tend to worp leaving puddles on roof.a hard wind going up the roof could cause a leak.4 look inside of copper box may need some tar from caulking gun(not as messy as trawl)5 if roof appers deteriorated replace roof.
there are ways of fixing roof puddling when installing a new lay over roof. call a roofer before inside becomes moldie you may not see it but it may be there.